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math.AP2024
A few sharp estimates of harmonic functions with applications to Steklov eigenfunctions
Xing Wang, Cheng Zhang
On smooth compact manifolds with smooth boundary, we first establish the sharp lower bounds for the restrictions of harmonic functions in terms of their frequency functions, by usi…
math.AP2024
Weyl laws for Schrödinger operators on compact manifolds with boundary
Xiaoqi Huang, Xing Wang, Cheng Zhang
We prove Weyl laws for Schrödinger operators with critically singular potentials on compact manifolds with boundary. We also improve the Weyl remainder estimates under the conditio…
math.AP2024
Restriction of Schrödinger eigenfunctions to submanifolds
Xiaoqi Huang, Xing Wang, Cheng Zhang
For Schrödinger operators with critically singular potentials on compact manifolds, we prove sharp estimates for the restriction of eigenfunctions to submanifolds.…